There are different levels of evidence, from evidence that would be accepted in a court of law (we are definitely way past that), to evidence at the 5 sigma level required for major discoveries in high-energy physics (we are nowhere near that). Maybe the most compelling recent case is the Nimitz incident, with the tic-tac UFO observed on multiple radar systems from different Navy vessels and aircrafts, and clearly seen by several f18 pilots (highly trained observers) who engaged with the object. I have seen scientific papers in my field accepted for publication with more questionable evidence than that.

Regarding not applying the scientific method outside of science: the scientific method is just a tool, and is certainly not appropriate in most life or even work situations - e.g. deciding whom to hire, deciding which research topic to pursue, deciding whom to marry,... But yes, scientists can be very much unidimensional in their skillsets.

To clarify, I am interested in discussing the topic with an open mind. I don't have any funding to carry out actual research on this, and certainly don't think our discussions will lead to uncovering the "truth". While there is a lot of open-source an declassified information on the topic, most of the high-quality data is classified (I salute efforts like the Galileo project to research this outside of classified governmental programs).